Analysis of queue with two phases of service and m phases of repair for server breakdown under N‐policy

The present paper deals with a single server queueing system wherein the customers join the system in bulk with varying arrival rates. The first stage regular service and second stage optional service are provided to the customers. The server may breakdown at any instant during any stage of service. There is a provision of essential and optional repair in m phases. To discuss the steady state behaviour of the system, the assumptions of probability reasoning and supplementary variable technique is employed. Various performance indices are obtained using the generating function approach. To verify the validity of these indices, the numerical illustrations are provided. The technique of principle of maximum entropy is also considered to find the approximate values of the system probabilities for the queue length distribution.